This is the 2095th most frequent Russian word.
октябрьском
"Октябрьском" is the prepositional form of the adjective "октябрьский," meaning "October" (related to October).
Here, 'октябрьском' is an adjective form in the prepositional case used to describe the district name 'Октябрьский', indicating a place.
Я посетил музей в Октябрьском районе в прошлом году.
I visited a museum in the October district last year.
In this sentence, 'октябрьском' is an adjective in the prepositional case describing 'праздник', showing temporal reference.
Во время октябрьском празднике мы гуляли по городу.
During the October holiday, we strolled around the city.
This sentence uses 'октябрьском' as an adjective in the prepositional case to describe the park, signifying a proper name or seasonal reference.